On torsion anomalous intersections

Checcoli, Sara and Veneziano, Francesco and Viada, Evelina. (2014) On torsion anomalous intersections. Rendiconti Lincei. Matematica e Applicazioni, 25 (1). pp. 1-36.

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A deep conjecture on torsion anomalous varieties states that if V is a weak-transverse variety in an abelian variety, then the complement V^{ta} of all V-torsion anomalous varieties is open and dense in V. We prove some cases of this conjecture. We show that the V-torsion anomalous varieties of relative codimension one are non-dense in any weak-transverse variety V embedded in a product of elliptic curves with CM. We give explicit uniform bounds in the dependence on V. As an immediate consequence we prove the conjecture for V of codimension two in a product of CM elliptic curves. We also point out some implications on the effective Mordell-Lang Conjecture.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger)
UniBasel Contributors:Veneziano, Francesco
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Accademia Nazionale dei Lincei
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:15 Nov 2017 08:43
Deposited On:20 Jun 2016 08:14

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